Scientific Method —

Crystals… made of time

Sometimes I know that I'm going to write about a paper before I even read it. The hook is simply too inviting. A new paper, simply entitled "Time crystals," with a companion paper "Quantum time crystals," is that sort of irresistible. Even if the papers turned out to be giant piles of steaming science, lying in full repugnant view on the pages of Physical Review Letters, it was certain there would be a good story to tell.

As it turns out, these papers are a strange brew of "what if," mixing the unlikely with the banal to create a heady mixture of pure confusion. As the names of the papers imply, the authors consider how it might be possible to create something akin to a crystal—but one that occupied time rather than space.

To a physicist, a crystal is a collection of basic building blocks, repeated in space. A salt crystal consists of a regular array of sodium and chlorine atoms. Wherever you are within the crystal, if you move by any multiple of a specific distance, you find yourself in a place that looks exactly the same. This is called translational symmetry.

So let's consider what this might mean in relation to time. In its crudest sense, it would mean that if we move forward or backward in time by some multiple of a fixed amount, we would find ourselves in exactly the same environment. My first thought upon encountering this idea: any wave would satisfy this criteria. You simply translate yourself in time by an integer of the oscillation period of the wave. But I had the feeling this wasn't what the authors, Shapere and Wilczek, had in mind.

The authors describe their crystal as a ruler, one that provides periodic landmarks in an otherwise featureless space. The periodicity introduced by the presence of the atoms allows us to measure the passage of space. Imagine sitting in a room where nothing ever appeared to change as time passes—you would have no way to measure the flow of time. But if the room were in a time crystal, you would still have a natural clock with which to observe the passage of time using its repetition.

Does this sound confusing? It should. It certainly confuses the hell out of me. Mathematically, the argument runs like so: If I take the math for describing a normal crystal and convert all the spatial variables into time variables, I get a set of solutions that tell me time crystals exist. That argument, though, uses the equations for the motion of a particle. If you switch to a different variable (momentum), then you find that a time crystal cannot exist.

Reality may be weird, but it usually arrives at self-consistency at some point. So why do time crystal simultaneously exist and not exist? The answer lies in the details of converting between the two descriptions. In the conversion process, we assume both descriptions of reality are smooth. Upon examination, however, it turns out that one of them has a point where certain values—envision the rate of change of momentum at the turning point of a swing—very suddenly approach infinity. Of course, it takes a very unusual swing to generate accelerations approaching infinity.

The key point is that this is anything but smooth. These infinities also occur at precisely the momentum predicted for a particle in a time crystal. Just to make matters more confusing, that particle has multiple energy values, despite having a single momentum.

All of this makes one think a time crystal must be something exotic and exciting. But in their companion paper, "Quantum time crystals," the authors use the example of a persistent current in a superconducting ring. The only difference between that and light circulating in a ring of glass is that the light will slowly be absorbed. But if I balance that loss with a little extra light from outside, do I have a time crystal? Can it really be as banal as that?

I know I am not the sharpest knife in the drawer. Indeed, if my students were given the chance to vote on the person in most dire need of beating with a clue stick, you wouldn't need Nate Silver to predict the outcome. But I can only conclude this paper is reporting something incredibly common (hey, the orbit of the Earth is a time crystal), but carefully obfuscated. Or, it is pure awesome, allowing the existence of particles with multiple values of energy for a single momentum state.

Alternatively, and this is most likely, the infinities that turn up in one of the descriptions are simply not physically realizable. We cannot create a swing with turning points sufficiently sharp to generate these infinities.

Chris Lee
Chris writes for Ars Technica's science section. A physicist by day and science writer by night, he specializes in quantum physics and optics. He lives and works in Eindhoven, the Netherlands. Emailchris.lee@arstechnica.com//Twitter@exMamaku

I'm somewhat amateurish in this field, but it brought to mind quantum states of particles and uncertainty. I could see that these changes to infinity could exist but be balanced out on a larger scale. It makes me consider that as we observe things in the macro (not quantum) world, it's really a combination of all these states that are averaged out (in a sense) to something that resembles a steady state. Sort of like how you can have a scatterplot that, viewed from a sufficient distance, appears to be a simple inclined line. Except the individual data points aren't necessarily finite states, but possibilities.

Time crystals sounds like an intriguing idea, but I can somewhat understand how quantum time crystals may not be able to exist when considered in certain ways.

Wherever you are within the crystal, if you move by any multiple of a specific distance, you find yourself in a place that looks exactly the same. This is called translational symmetry.

So let's consider what this might mean in relation to time. In its crudest sense, it would mean that if we move forward or backward in time by some multiple of a fixed amount, we would find ourselves in exactly the same environment.

But then isn't every spatial crystal also a time-crystal? After all, the repeating "environment" is still space, not time. So if I'm in a salt crystal, I look around and then we both go forwards/backwards in time, the salt crystal will look the same after my "time travel".

For the record, a time crystal is a trivial construction in a specific frame of reference. Place an object on the table next to you, and point a camera at it. Check the image. Check again in ten second. Looks the same, doesn't it. Ten more seconds. Sense a pattern forming here? Crystals in space do eventually end, and this "time crystal" ends when you move the object.

If you require periodicity in your crystals, just ensure that the object is a metronome. The "crystal" structure ends when the metronome is moved or winds down.

The authors describe their crystal as a ruler, one that provides periodic landmarks in an otherwise featureless space. The periodicity introduced by the presence of the atoms allows us to measure the passage of space.

So, WRT the salt crystal, what is the "periodicity"?

I could understand if they had marker C14 (made after 774 thank you), but in the absence of something that changes in some predictable fashion with the passage of time, I don't see any marker.

Is this a subject best studied with the aid of medicinal alcohol? Say, a good Irish whiskey (OK, a cheap Irish whiskey, it was what I could afford)?

The part about requiring infinite acceleration/momentum sounds kind of like this: if we could give a particle infinite acceleration, then it could acquire infinite momentum, and end up as kind of a standing-wave-in-time or possibly move forward/backward in time, as everything would seem to be the same? Isn't that kind of like a photon that moves at the speed of light, and experiences no time and no change until it impacts something?

1. has to be in its lowest energy state, so I don't think the earth in orbit counts.

2. a proposed physical example is a ring of ions circulating in an ion trap. Of course, that's in reference to the concept of a SPACE-time crystal, and, in the article, you refer specifically to a TIME-crystal that behaves as a crystal exclusively in time RATHER than in space.

Hmmm...When I think of an object, crystal or not, that exists in a fluid time and fixed space, I imagine an object that could never be moved. It would not age, nor decompose in any way. It would just be there, no matter what was going on around it. No matter if it was 1900 or 2500, it would still be exactly the same as if it had never aged, had been created and placed in its spot not but a moment ago, and yet could be found in its exact same state millions of years in the past or future. Such a crystal could act as a gateway, or possibly an anchor point for time travel. A portal if you will, that also could act as a looking glass into the past or future. Or, a communication device.

Edit: To add to this, part of the article where it describes "Wherever you are within the crystal, if you move by any multiple of a specific distance, you find yourself in a place that looks exactly the same. This is called translational symmetry." I think is looking too much at the crystal itself from a space perspective, our own reality. If you translate the spacial aspect of a crystal fixed in time(as we all are now) to a perspective where the crystal or object was fixed in space instead of time, that could imply a time traveling crystal which would only exist as a pattern in time, not in space. As such, it would repeat itself over a time period, only existing spatially for specific times, the specifics of such time periods recurring in some sort of pattern, but always in the same place. So, a time crystal as described would be any object that existed in a specific(Im assuming relative) location that never changed, and only at specific times that recurred over and over again in a pattern from our own fixed time/fluid space perspective. The concept reminds me of various sci fi plots where there is some religious(or otherwise significant) object that could only be found at a specific place and at a specific time, one that recurs only every 500 or 5000 or 500,000 years, and only exists for a very specific window.

Of course though, Im not a physicist nor mathematician and am only trying to imagine what is being described.

Edit2: Oh great, my brain is starting to smolder lol.

Another concept Ive read about, and am now brought back to, could inddicate that WE are actually time crystals, at the quantum level anyway. We know that at the quantum level our atoms etc are actually blinking in and out of existence, possibly in a pattern. This blinking occurs so rapidly, our brains cannot process the difference. Its the same as a TV screen which refreshes 60 times a second. We see nothing more than a fluid motion, images that progress through time. We can not detect the Vblank. Reality could work the same way, with our minds and bodies being fixed in space, but moving through time by blinking in and out from one nano second to the next, so fast that our brains are given the illusion of being fixed in time and moving through space, when in reality, spacial movement is only achieved via time travel, by blinking in and out of relative existence.